Abstract
The starting point of this paper is the construction of a general family \left( L_{n}\right) _{n\geq 1} of positive linear operators of discrete type. Considering L_{n\left( k\geq 1\right) }^{k} the sequence of iterates of one of such operators,L_{n} our goal is to find an expression of the upper edge of the error \left \Vert L_{n}^{k}f-f^{\ast }\right \Vert ,f\in\left[ 0,1\right],where f^{\ast }, is the fixed point of L_{n}.The estimate makes use of the error formula for the sequence of successive approximations in Banach’s fixed point theorem and the error of approximation of the operator L_{n}.Examples of special operators are inserted. Some extensions to multidimensional approximation operators are also given.
Authors
Octavian Agratini
Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy, Romania
Radu Precup
Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy, Romania
Faculty of Mathematics and Computer Science and Institute of Advanced Studies in Science and Technology, Babeş-Bolyai University, Cluj-Napoca, 400084, Romania
Keywords
Positive linear operator; Bernstein operator; Stancu operator; Cheney–Sharma operator; Banach fixed point theorem; Perov fixed point theorem
Paper coordinates
O. Agratin, R. Precup, Estimates related to the iterates of positive linear operators and their multidimensional analogues, Positivity, 28 (2024) art. no. 27,
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